For me, typical aftermarket speakers will not produce nearly low enough or any quality sounding bass. They are designed for midrange frequencies and will not excel at low-end bass. To get the low end punch you are looking for I would highly recommend getting a subwoofer.
However, many people are happy with the bass produced from their speakers. So if you are already have the equipment then you might as well hook it up and see if the bass is sufficient for your tastes. If it is not then you can always add a sub down the road.
I understand that you don't want loud car shaking bass. That does not mean that all subs will give you that. You could simply get a sub designed to just add a little bit of low end to your system.
Spanky, playing low frequencies through speakers will not damage them. Speakers can play any frequency. They just will not play the lower frequencies very well which will result in poor bass response.
Good Luck!!!